This phase I trial studies the side effects and best dose of veliparib when given together with floxuridine in treating patients with epithelial ovarian, primary peritoneal cavity, or fallopian tube cancer that has spread to other places in the body. Veliparib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as floxuridine, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving veliparib together with floxuridine may kill more tumor cells.